The gamut of dynamic logics

  title={The gamut of dynamic logics},
  author={Jan van Eijck and Martin Stokhof},
  booktitle={Logic and the Modalities in the Twentieth Century},

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  • V. Pratt
  • Computer Science, Philosophy
    FOCS 1976
  • 1976
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A Theory of Type Polymorphism in Programming

  • R. Milner
  • Computer Science
    J. Comput. Syst. Sci.
  • 1978

Structural Operational Semantics

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